Prediction of Transonic LCOs using an Aeroelastic Harmonic Balance Method

This work proposes a novel approach to compute transonic Lim
it Cycle Oscillations using high fidelity analysis. CFD based Harmonic Balance methods have proven to be efficient tools to predict periodic phenomena. This paper’s contribution is to present a new methodology to determine the unknown frequency of oscillations, enabling HB methods to accurately capture Limit Cycle Oscillations (LCOs); this is achieved by defining a frequency updating procedure based on a coupled CFD/CSD Harmonic Balance formulation to find the LCO condition. A pitch/plunge aerofoil and delta wing aerodynamic and respective linear structural models are used to validate the new method against conventional time-domain simulations. Results show consistent agreement between the proposed and time-marching methods for both LCO amplitude and frequency, while producing at least one order of magnitude reduction in computational time.

Transonic Nonlinear Aeroelastic Simulations Using An Harmonic Balance Method

This paper presents an approach to compute transonic Limit Cycle O
scillations using a coupled Harmonic Balance formulation based on the Euler equations for fluid dynamics and finite element models. The paper will investigate the role of aerodynamic (shocks) and structural nonlinearities in driving the limit cycle behaviour. Part icular attention will be given to nonlinear interactions for subcritical LCOs. The Aero elastic Harmonic Balance formulation, allows for solutions of the coupled structural dynamics and CFD system at a reduced cost.

Prediction of Limit Cycle Oscillations Using an Implicit Aeroelastic-Harmonic Balance Method

This work proposes a extends a novel approach to compute tran sonic Limit Cycle Oscillations using high fidelity analysis. CFD based Harmonic Balance methods have proven to be efficient tools to predict periodic phenomena. This paper’s contribution is to present a methodology to determine the unknown frequency of oscillations using an implicit for- mulation of the HB method to accurately capture Limit Cycle Oscillations (LCOs); this is achieved by defining a frequency updating procedure based on a coupled CFD/CSD Harmonic Balance formulation to find the LCO condition. A pitch/plunge aerofoil and respective linear structural models is used to exercise the new method. Results show consistent agreement between the proposed and time-marching methods for both LCO amplitude and frequency.

Investigation of Limit Cycle Oscillations Using Aeroelastic-Harmonic Balance Method

This work investigates limit cycle oscillations in the transonic regime. A novel approach to predict Limit Cycle Oscillations using high fidelity analysis is exploited to accelerate calculations. The method used is an Aeroeasltic Harmonic Balance approach, which has been proven to be efficient and able to predict periodic phenomena. The behaviour of limit cycle oscillations is analysed using uncertainty quantification tools based on polynomial chaos expansions. To improve the efficiency of the sampling process for the polynomial-chaos expansions an adaptive sampling procedure is used. These methods are exercised using two problems: a pitch/plunge aerofoil and a delta-wing. Results indicate that Mach n. variability is determinant to the amplitude of the LCO for the 2D test case, whereas for the wing case analysed here, variability in the Mach n. has an almost negligible influence in amplitude variation and the LCO frequency variability has an almost linear relation with Mach number. Further test cases are required to understand the generality of these results.

Prediction of limit cycle oscillations under uncertainty using a Harmonic Balance method

The Harmonic Balance method is an attractive solution for computing periodic responses and can be an alternative to time domain methods, at a reduced computational cost. The current paper investigates using a Harmonic Balance method for simulating limit cycle oscillations under uncertainty. The Harmonic Balance method is used in conjunction with a non-intrusive polynomial-chaos approach to propagate variability and is validated against Monte Carlo analysis. Results show the potential of the approach for a range of nonlinear dynamical systems, including a full wing configuration exhibiting supercritical and subcritical bifurcations, at a fraction of the cost of performing time domain simulations.

Prediction of Transonic Limit-Cycle Oscillations Using an Aeroelastic Harmonic Balance Method

This work proposes a novel approach to compute transonic limit-cycle oscillations using high-fidelity analysis. Computational-Fluid-Dynamics based harmonic balance methods have proven to be efficient tools to predict periodic phenomena. This paper’s contribution is to present a new methodology to determine the unknown frequency of oscillations, enabling harmonic balance methods to accurately capture limit-cycle oscillations; this is achieved by defining a frequency-updating procedure based on a coupled computational-fluid-dynamics/computational-structural-dynamics harmonic balance formulation to find the limit-cycle oscillation condition. A pitch/plunge airfoil and delta wing aerodynamic and respective linear structural models are used to validate the new method against conventional time-domain simulations. Results show consistent agreement between the proposed and time-marching methods for both limit-cycle oscillation amplitude and frequency while producing at least a one-order-of-magnitude reduction in computational time.

Even order harmonic Series-L/Parallel-Tuned Class-E frequency multiplier

In this brief, we propose a new Class-E frequency multiplier based on the recently introduced Series-L/Parallel-Tuned Class-E amplifier. The proposed circuit produces even-order output harmonics. Unlike previously reported solutions the proposed circuit can operate under 50% duty ratio which minimizes the conduction losses. The circuit also offers the possibility for increased maximum operating frequency, reduced peak switch voltage, higher load resistance and inherent bond wire absorption; all potentially useful in monolithic microwave integrated circuit implementations. In addition, the circuit topology suggested large transistors with high output capacitances can be deployed. Theoretical design equations are given and the predictions made using these are shown to agree with harmonic balance circuit simulation results.

Exploring figures of merit associated with the suboptimum operation of class-E power amplifiers

Closed-form design equations for the operation of a class-E amplifier for zero switch voltage slope and arbitrary duty cycle are derived. This approach allows an additional degree of freedom in the design of class-E amplifiers which are normally designed for 50 duty ratio. The analysis developed permits the selection of non-unique solutions where amplifier efficiency is theoretically 100 but power output capability is less than that the 50 duty ratio case would permit. To facilitate comparison between 50 (optimal) and non-50 (suboptimal) duty ratio cases, each important amplifier parameter is normalised to its corresponding optimum operation value. It is shown that by choosing a non-50 suboptimal solution, the operating frequency of a class-E amplifier can be extended. In addition, it is shown that by operating the amplifier in the suboptimal regime, other amplifier parameters, for example, transistor output capacitance or peak switch voltage, can be included along with the standard specification criteria of output power, DC supply voltage and operating frequency as additional input design specifications. Suboptimum class-E operation may have potential advantages for monolithic microwave integrated circuit realisation as lower inductance values (lower series resistance, higher self-resonance frequency, less area) may be required when compared with the results obtained for optimal class-E amplifier synthesis. The theoretical analysis conducted here was verified by harmonic balance simulation, with excellent agreement between both methods. © The Institution of Engineering and Technology 2007.

Convergence acceleration of the doubly periodic Green's function for the analysis of thin wire arrays

A method is proposed to accelerate the evaluation of the Green's function of an infinite double periodic array of thin wire antennas. The method is based on the expansion of the Green's function into series corresponding to the propagating and evanescent waves and the use of Poisson and Kummer transformations enhanced with the analytic summation of the slowly convergent asymptotic terms. Unlike existing techniques the procedure reported here provides uniform convergence regardless of the geometrical parameters of the problem or plane wave excitation wavelength. In addition, it is numerically stable and does not require numerical integration or internal tuning parameters, since all necessary series are directly calculated in terms of analytical functions. This means that for nonlinear problem scenarios that the algorithm can be deployed without run time intervention or recursive adjustment within a harmonic balance engine. Numerical examples are provided to illustrate the efficiency and accuracy of the developed approach as compared with the Ewald method for which these classes of problems requires run time splitting parameter adaptation.

Analysis and Design of Class-E3F and Transmission-Line Class-E3F2 Power Amplifiers

In this paper, analysis and synthesis approach for two new variants within the Class-EF power amplifier (PA) family is elaborated. These amplifiers are classified here as Class-E3 F2 and transmission-line (TL) Class-E3 F 2. The proposed circuits offer means to alleviate some of the major issues faced by existing topologies such as substantial power losses due to the parasitic resistance of the large inductor in the Class-EF load network and deviation from ideal Class-EF operation due to the effect of device output inductance at high frequencies. Both lumped-element and transmission-line load networks for the Class-E 3 F PA are described. The load networks of the Class-E3 F and TL Class-E 3 F2amplifier topologies developed in this paper simultaneously satisfy the Class-EF optimum impedance requirements at fundamental frequency, second, and third harmonics as well as simultaneously providing matching to the circuit optimum load resistance for any prescribed system load resistance. Optimum circuit component values are analytically derived and validated by harmonic balance simulations. Trade-offs between circuit figures of merit and component values with some practical limitations being considered are discussed. © 2010 IEEE.

The Influence of Structural Modeshape Variability on Limit Cycle Oscillation Behaviour

Modal analysis is a popular approach used in structural dynamic and aeroelastic problems due to its efficiency. The response of a structure is compo
sed of the sum of orthogonal eigenvectors or modeshapes and corresponding modal frequencies. This paper investigates the importance of modeshapes on the aeroelastic response of the Goland wing subject to structural uncertainties. The wing undergoes limit cycle oscillations (LCO) as a result of the inclusion of polynomial stiffness nonlinearities. The LCO computations are performed using a Harmonic Balance approach for speed, the modal properties of the system are extracted from MSC NASTRAN. Variability in both the wing’s structure and the store centre of gravity location is investigated in two cases:- supercritical and subcritical type LCOs. Results show that the LCO behaviour is only sensitive to change in modeshapes when the nature of the modes are changing significantly.

Analysis of Transonic Limit Cycle Oscillations under Uncertainty

For the computation of limit cycle oscillations (LCO) at transonic speeds, CFD is required to capture the nonlinear flow features present. The Harmonic Balance method provides an effective means for the computation of LCOs and this paper exploits its efficiency to investigate the impact of variability (both structural a nd aerodynamic) on the aeroelastic behaviour of a 2 dof aerofoil. A Harmonic Balance inviscid CFD solver is coupled with the structural equations and is validated against time marching analyses. Polynomial chaos expansions are employed for the stochastic investiga tion as a faster alternative to Monte Carlo analysis. Adaptive sampling is employed when discontinuities are present. Uncertainties in aerodynamic parameters are looked at first followed by the inclusion of structural variability. Results show the nonlinear effect of Mach number and it’s interaction with the structural parameters on supercritical LCOs. The bifurcation boundaries are well captured by the polynomial chaos.

Reducing Parametric Uncertainty in Limit Cycle Oscillations

The assimilation of discrete higher fidelity data points with model predictions can be used to achieve a reduction in the uncertainty of the model input parameters which generate accurate predictions. The problem investigated here involves the prediction of limit-cycle oscillations using a High-Dimensional Harmonic Balance method (HDHB). The efficiency of the HDHB method is exploited to enable calibration of structural input parameters using a Bayesian inference technique. Markov-chain Monte Carlo is employed to sample the posterior distributions. Parameter estimation is carried out on both a pitch/plunge aerofoil and Goland wing configuration. In both cases significant refinement was achieved in the distribution of possible structural parameters allowing better predictions of their
true deterministic values.